The modern solution to the logbook backup problem is to go digital. I recommend
http://onlinelogbook.net, as it allows you to import/export your logbook data in a sane format. It also has a feature that makes "digitalizing" from paper a lot more streamlined.
Personally, I used a paper logbook up until I started Instructing. As an instructor, I realized my dinky "student" logbook was going to fill up in about 2 weeks, so instead of buying another paper logbook, I decided to go digital. I then began logging all flights into logshare.com because at the time it seemed to be the best solution. Geographical redundancy, a backup system, accessible from anywhere, easy to compile stats and totals, etc. After a I discovered onlinelogbook.net, I just imported my entire logbook over to it, since it's a better system. I don't know what I would have done had I originally digitalized with one of those "digital logbook" software thingies that don't have any way to migrate the data.